Superposition of Waves — Flashcards

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A progressive wave is a disturbance that travels continuously through a medium without any damping or obstruction. The displacement equation is: y(x,t) = A sin(kx - ωt) for rightward motion and y(x,t)…

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When a transverse wave reflects from a fixed end or denser medium: (1) A crest reflects as a trough and vice versa, (2) There is a phase change of π radians, (3) The amplitude remains the same. This o…

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When two or more waves traveling through a medium pass through a common point, each wave produces its own displacement at that point independently. The resultant displacement at that point is the vect…

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For waves y₁ = A₁ sin ωt and y₂ = A₂ sin(ωt + φ), the resultant amplitude is: A² = A₁² + A₂² + 2A₁A₂ cos φ. Maximum amplitude (φ = 0): A = A₁ + A₂. Minimum amplitude (φ = π): A = |A₁ - A₂|. This deter…

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A stationary wave is formed when two identical waves of same amplitude and frequency travel in opposite directions and interfere. The equation is: y = 2a cos(2πx/λ) sin(2πnt). It has fixed points call…

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For stationary wave y = 2a cos(2πx/λ) sin(2πnt): Nodes (minimum amplitude): x = (2n-1)λ/4 where n = 1,2,3... Antinodes (maximum amplitude): x = nλ/2 where n = 0,1,2,3... Distance between consecutive n…

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Given: l = 105 cm = 1.05 m, 3 loops, f = 15 Hz. For 3 loops: l = 3λ/2, so λ = 2l/3 = 2(1.05)/3 = 0.70 m. Wave speed: v = fλ = 15 × 0.70 = 10.5 m/s…

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Closed pipe (one end closed): Node at closed end, antinode at open end. Only odd harmonics present: f = (2n-1)v/4L. Open pipe (both ends open): Antinodes at both open ends. All harmonics present: f = …